Precalculus

How do you determine if arcsin(sin(-2π/7))=-2π/7?

  1. 👍 0
  2. 👎 0
  3. 👁 44
asked by jy
  1. in general
    arcsin(sinx) = x , since the operations are inverses of each other

    However, since arcsinØ has no unique answer, it is common practise to state the solution closest to zero

    e.g. suppose you do arcsin(sin 200°) on your calculator
    sin 200° = -.342...
    and arcsin(200°)
    = arcsin (-.342..) = -20° , which is correct since sin(-20) = -.342...
    Also using the CAST rule, we know sin 200° = sin(-20°) or -sin20°

    Since -2π/7 is in quadrant IV (appr -64°)
    arcsin(sin(-2π/7)) = -2π/7

    try it on your calculator, make sure you set it to radians

    1. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1

    asked by Anonymous on August 3, 2007
  2. Trigonometry

    Evaluate please: a.) arcsin(sin 13pi/16) b.) arccos(cos[-pi/18]) c.) arcsin(sin pi/18 d.) arcsec(-√2) e.) arctan(-√3/3)

    asked by Liv on November 26, 2016
  3. Trigonometry

    I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b))

    asked by Jen on July 27, 2007
  4. Calculus

    Find the exact value of cot(arcsin(12/13)) and cos(arcsin(1.7/2)) I know that cos(arcsin(x))=sin(arccos(x))=sqrt(1-x^2). I'm having more difficulty with the first one. Please help! Thank you

    asked by Emily on April 1, 2016
  5. maths 2

    The original question I had was write arcsin4 in the form a+ib. I manage and understand how to get so far BUT How do I get from cosacoshb-isinasinhb=4 to 2m(pi)+/- iarccosh4 arcsin4 = a + b i ---> 4 = sin(a + bi) sin(a + bi) =

    asked by Jake on January 14, 2007
  6. maths

    Please can you help me with this question? Choose the option which is a false statement: A arctan(tan2/3pi))=-1/3pi B arccos(cos(3/4pi))=3/4pi C sin(arcsin(-1/2pi))=-1/2pi D arcsin(1/2squareroot3)=1/3pi E arcsin(sin(3/4pi))=1/4pi

    asked by janet on May 26, 2011
  7. MATH

    I am given arcsin (sin 4pi) do the arc sin and sin cancel out? How do we solve this?

    asked by MONDAY on November 6, 2017
  8. Calc.

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x)

    asked by Chelsea on March 9, 2011
  9. calculus

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x)

    asked by Chelsea on March 10, 2011
  10. Calculus

    s=çdx/(4+5cos x). By using t-substitution, i.e. t=tan(x/2) we get cos x=(1-t^2)/(1+t^2) and dx=2dt/(1+t^2). Substituting in s and simplifying, we get s= 2çdt/4(1+t^2)+5(1-t^2)=2çdt/(9-t^2). Using standard result

    asked by MS on October 30, 2013
  11. Math

    Find the exact value of sin(A+B) when angle A is arcsin(8/17) and angle B is arcsin(5/13)

    asked by Jason Q. on September 7, 2014

More Similar Questions